I am a bit struggling with choosing which test I should apply to my data.

My dependent variable is continuous (participants could score between 0 and 6) and I have three factors:

1) a nominal variable with two categories (namely "native" and "nonnative")

2) a nominal variable with four categories (namely four different culture groups)

3) a continuous variable (namely a proficiency score). BUT I expect that the relationship between the DV and this variable is exponential.

So, I am a bit lost… Should I ignore my expectation that the relationship between my DV and IV3 is might be exponential, and just apply a linear regression?

Many thanks for your help!